Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Algebra
Cover of the book Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups by Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli, Cambridge University Press
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Author: Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli ISBN: 9781107721241
Publisher: Cambridge University Press Publication: January 16, 2014
Imprint: Cambridge University Press Language: English
Author: Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
ISBN: 9781107721241
Publisher: Cambridge University Press
Publication: January 16, 2014
Imprint: Cambridge University Press
Language: English

This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

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This book presents an introduction to the representation theory of wreath products of finite groups and harmonic analysis on the corresponding homogeneous spaces. The reader will find a detailed description of the theory of induced representations and Clifford theory, focusing on a general formulation of the little group method. This provides essential tools for the determination of all irreducible representations of wreath products of finite groups. The exposition also includes a detailed harmonic analysis of the finite lamplighter groups, the hyperoctahedral groups, and the wreath product of two symmetric groups. This relies on the generalised Johnson scheme, a new construction of finite Gelfand pairs. The exposition is completely self-contained and accessible to anyone with a basic knowledge of representation theory. Plenty of worked examples and several exercises are provided, making this volume an ideal textbook for graduate students. It also represents a useful reference for more experienced researchers.

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